Question 6
A beaver and a bear cut long logs into pieces. The beaver makes one cut per minute. The bear has two saws and can simultaneously make two cuts 1 metre apart. They may work at the same time, but not on the same log. Each cutting operation takes one minute. A beaver can split 7 m into 1 m and 6 m; a bear can split 7 m into 2 m,1 m,4 m.
The beaver alone loads 7 metres of finished pieces onto the truck per minute; the bear cannot help load. Today there are three 7-metre logs, to be made into nine 1-metre pieces, three 2-metre pieces and two 3-metre pieces. What is the shortest total cutting-and-loading time?
Editorial scheduling convention: each loading operation occupies the beaver for one full minute and loads up to 7 metres of pieces already finished before that operation begins. Cutting and loading cannot overlap for the beaver.
The beaver alone loads 7 metres of finished pieces onto the truck per minute; the bear cannot help load. Today there are three 7-metre logs, to be made into nine 1-metre pieces, three 2-metre pieces and two 3-metre pieces. What is the shortest total cutting-and-loading time?
Editorial scheduling convention: each loading operation occupies the beaver for one full minute and loads up to 7 metres of pieces already finished before that operation begins. Cutting and loading cannot overlap for the beaver.